The development of wireless communication equipments and the continuous increase of the speed of the connections calls for advanced equalization methods. Indeed, the performance of wireless receivers tends to be severely impacted by fast time-varying propagation channels causing interference as well as the interference signal coming from the other wireless equipments.
Considering, for instance, the general signal modelr=Hs+v 
With s being the desired signal sequence, H being the propagation convolution matrix and v being the additive white Gaussian noise.
One known reference equalization method providing near-optimum performance is the well known Minimum Mean Square Error (MMSE) complying with the following—also well known—formulas:ŝMMSE=UHr=(HHH+σv2I)−1HHr (HHH+σv2I)ŝMMSE=HHr 
Where U corresponding to the equalization matrix;
σv correspond to the variance of the noise;
I correspond to the Identity matrix
Generally speaking, communications systems designers usually attempt to embody the MMSE receiver which clearly which is the nearly-optimal receiver and yields a more accurate estimation which shows to be a satisfactory trade-off between ICI equalization and noise enhancement.
However, the implementation of MMSE equalization requires, as recalled above, the inversion of a matrix(HHH +σv2I)
Which inversion involves a condition number of the order of K(HHH), thus entailing a significant amount of processing resources as well as a also non negligible amount of storage for the implementation of the MMSE receiver.
In the particular case where the H matrix is full rank—which is a general situation in practice—a second well-known equalization model can be considered, which is the so-called Zero-forcing (ZF) having a first advantage of not requiring any knowledge of the noise and, above all, which allows the equalizer to be simplified as shown below:ŝZF=(HHH)−1HHr ŝZF=H−1r if H is full rank(HHH)ŝZF=HHr HŝZF=r 
The formula above recalls that the ZF receiver only requires the inversion of matrix H, corresponding to a computation having a condition number of K(H) only, and certainly not K(HHH) which was the case for the conventional MMSE technique.
Indeed, the problem of approximating the inverse of H is inherently better conditioned than the one of inverting HHH by observing the relation of their respective condition numbers (CN):K(H)<K(HHH).
As it is well-known from the literature the smaller the CN, the faster an iterative algorithm will converge
So far, there has been a dilemma residing in the choice between, on one hand, accuracy of the equalization technique (MMSE) and, on the other hand, the complexity of the algorithm to be considered for embodying the equalizer (K(HHH) or K(H)).
Document “LOW-COMPLEXITY TIME-DOMAIN ICI EQUALIZATION FOR OFDM COMMUNICATIONS OVER RAPIDLY VARYING CHANNELS” by Thomas Hrycak and Gerald Matz shows a first attempt to achieve MMSE time domain equalization for an OFDM system with relative reduced complexity. For that purpose, an iterative LSQR algorithm is being used, which shows some drawbacks in particular because of the high amount of storage being required for embodying the LSQR.
Therefore, there is a wish for more advanced receiver equalization techniques to mitigate the effect of the interference and noise, achieving MMSE equalization with reduced complexity, of the order of K(H) only.